varSampStable | RawTree

Calculate the sample variance of a data set. Unlike varSamp, this function uses a numerically stable algorithm. It works slower but provides a lower computational error.

The sample variance is calculated using the same formula as varSamp:

$$ \frac{\Sigma{(x - \bar{x})^2}}{n-1} $$

Where:

$x$ is each individual data point in the data set
$\bar{x}$ is the arithmetic mean of the data set
$n$ is the number of data points in the data set

Syntax

varSampStable(x)

Arguments

x — The population for which you want to calculate the sample variance. (U)Int* or Float* or Decimal*

Returned value

Returns the sample variance of the input data set. Float64

Examples

Computing stable sample variance

DROP TABLE IF EXISTS test_data;
CREATE TABLE test_data
(
    x Float64
)
ENGINE = Memory;

INSERT INTO test_data VALUES (10.5), (12.3), (9.8), (11.2), (10.7);

SELECT round(varSampStable(x),3) AS var_samp_stable FROM test_data;

┌─var_samp_stable─┐
│           0.865 │
└─────────────────┘

Introduced in version 1.1.